The invention relates to the field of optical filters, and more particularly optical filters used for dropping or adding wavelengths in wavelength division multiplex (WDM) optical fiber transmission systems. Such filters are referred to as optical add-and-drop multiplexers (OADMs).
WDM transmission uses optical filters having a transfer function that is as rectangular as possible, and suitable for use over a broad band; typically, WDM multiplexers operate around 1550 nm and extend over a wavelength range of 25 nm to 100 nm. An ideal filter would present phase that is linear, i.e. group delay time that is constant, with no chromatic dispersion.
For these purposes, proposals have been made to use Bragg gratings written in the fibers. Such gratings are formed in a fiber by periodic or substantially periodic modulation of the index of the fiber. The term xe2x80x9cpitchxe2x80x9d is used to designate the modulation period along the fiber. It is possible with Bragg gratings to obtain a spectral response that is practically ideal, i.e. close to that which is desired. However, under such circumstances, the phase response of the filter becomes less and less linear towards the edges of the filter, so its dispersion becomes large, and as a result its usable bandwidth is much less than the total bandwidth of the filter.
Thus, L. R. Chen and P. W. E. Smith in xe2x80x9cFiber Bragg grating transmission filters with near-ideal filter responsexe2x80x9d, Electronics Letters, Vol. 34, No. 21, October 1998, pp. 2048-2050, propose filters that present xe2x80x9cchirpxe2x80x9d, i.e. in which pitch varies along the filter. More precisely, that article investigates the phase response of the filters, i.e. constant group velocity and zero dispersion, and it proposes using a filter made up of two superposed Bragg gratings, each presenting chirp that is linear.
Proposals have also been made to apodize the filter, i.e. to vary the modulation index of the fiber as a function of its length. By way of example, T. A. Strasser et al. in xe2x80x9cUV-induced fiber grating OADM devices for efficient bandwidth utilizationxe2x80x9d, OFC""96, PD8-2 to PDB-4, propose a filter having Gaussian apodization, i.e. the envelope of the index modulation function of the fiber is Gaussian. The filter does not present chirp, and the modulation pitch is constant.
B. J. Eggleton et al. in xe2x80x9cImplications of fiber grating dispersion for WDM communication systemsxe2x80x9d, IEEE Photonics Technology Letters, Vol. 9, No. 10, October 1997, pp. 1403-1405, state that apodization is a solution that enables crosstalk to be reduced between channels in filters for WDM optical fiber transmission systems. That article raises the problem of the chromatic dispersion caused by apodized filters, and proposes a compromise between filter characteristics and filter-induced dispersion, for apodization that is Gaussian or super-Gaussian.
The invention proposes a filter for a WDM optical fiber transmission system, and in particular for a dense WDM (DWDM) optical fiber transmission system, which presents simultaneously good spectral response and also dispersion within the passband of the filter that is acceptable.
More precisely, the invention provides a variable pitch Bragg grating having pitch, expressed as a function of distance, which is upwardly concave over a first portion of the grating and downwardly concave over a second portion of the grating.
Preferably, the function is of zero slope at the ends of the grating.
In an embodiment, the first portion extends over one half of the grating, and the second portion extends over the other half of the grating.
Preferably, the pitch is expressed as a quadratic function of distance over the first portion, and as a quadratic function of distance over the second portion.
In another embodiment, over the first portion, the pitch is expressed as a function of distance that is a polynomial of degree less than 6 and, over the second portion, as a function of distance that is a polynomial of degree less than 6.
In yet another embodiment, the pitch is expressed as a linear function of distance over a third portion of the grating extending between said first and second portions.
Preferably, the tangent to the curve giving pitch as a function of distance presents, at each end of the grating, and over a distance of less than 10% the length L of the grating, a slope whose absolute value is less than half the ratio (xcex9maxxe2x88x92xcex9min)/L of pitch variation over the length of the grating.
In an embodiment, the grating presents variation in chromatic dispersion lying in a range of xc2x1150 ps/nm over a wavelength bandwidth equal to at least half its xe2x88x923 dB bandwidth.
It is also advantageous for the ratio between the xe2x88x923 dB width and the xe2x88x9230 dB width to lie in the range 0.5 to 1.
Advantageously, the attenuation in reflection at 25 GHz from the center wavelength of the filter is greater than 30 dB, and preferably greater than 35 dB. In addition, the attenuation in transmission at the center wavelength of the filter is less than 0.05 dB.
The apodization can be super-Gaussian apodization with an a coefficient in the range [0.5; 1] or Blackman apodization with a Blackman coefficient in the range ]0; 0.2[, or indeed hyperbolic tangent apodization with a coefficient in the range ]0; 1[.
The invention also provides an optical filter for such a Bragg grating, and a WDM transmission system including at least one such Bragg grating.